Real cases
A case · you decide
Order of magnitude and Dimensional analysis check a viral claim
Order of magnitude & Dimensional analysis — a 17-year-old fact-checking a post for the school paper
A viral post says one electric-car battery (about 75 kWh) could power a city of a million homes for a day. Ravi wants to check it before the paper repeats it.
Dimensional analysis first: energy is kWh on both sides, so the comparison is fair. A typical home uses about 30 kWh a day.
Then count powers of ten on each side: a million homes at 30 kWh each, against one 75 kWh battery.
How far off is the claim?
Most wrong numbers are not a little wrong. They are wrong by powers of ten, and that is easy to check.
A case · you decide
The Brier score and Order of magnitude grade a forecast
The Brier score & Order of magnitude — a 16-year-old in a forecasting club scoring last month's predictions
Before the vote, Zara said she was 99% sure a school budget claim was exaggerated by at least 100 times. Lucas said 70%. The claim turned out to be only about three times too high.
The Brier score is (your probability − what happened)². Here the event ("exaggerated 100×") did not happen, so it scored 0.
Zara gave 0.99 and Lucas gave 0.70. Lower Brier scores are better.
What does the scoring say?
Say how sure you are, not how sure you want to be. The score keeps track.